Re: [eigen] Status of the eigen solver

["Gael Guennebaud" <gael.guennebaud@xxxxxxxxx>]

FYI:

[12:18] <CIA-20> ggael * r866561 eigen2/trunk/kdesupport/eigen2/ (Eigen/src/QR/EigenSolver.h test/eigensolver.cpp):
[12:18] <CIA-20> Fixes in Eigensolver:
[12:18] <CIA-20> * eigenvectors => pseudoEigenvectors
[12:18] <CIA-20> * added pseudoEigenvalueMatrix
[12:18] <CIA-20> * clarify the documentation
[12:18] <CIA-20> * added respective unit test
[12:18] <CIA-20> Still missing: a proper eigenvectors() function.

would be nice to get a proper eigenvectors() function before 2.0, anybody ?

also the current implementation actually comes from: "Algol procedure hqr2,  by Martin and Wilkinson, Handbook for Auto. Comp.,  Vol.ii-Linear Algebra, and the corresponding  Fortran subroutine in EISPACK", so I guess we can find further information about this issue there.

Cheers,
gael.

On Thu, Sep 25, 2008 at 3:15 AM, Benoît Jacob <jacob@xxxxxxxxxxxxxxx> wrote:

OK I see...

This seems like a very clever idea, but I am uncomfortable with that stuff
being called eigenvectors and eigenvalues, since that's not exactly what it
is. I'm all for it as long as it has a slightly different name.

Unless, someone explains me how this variant is what's actually useful in most
applications.

Personnally I don't see any urgent need for that (though it interests me
highly) so Gael if you're too busy you can ifdef that out for the 2.0
release, no problem. Somebody will eventually step up to help ;)

I just think this must be sorted out cleanly before it enters our stable API.

Cheers,
Benoit

PS we're mentioned here,
http://www.gamedev.net/community/forums/topic.asp?topic_id=509161&whichpage=1&#3318752

On Thursday 25 September 2008 02:48:44 Gael Guennebaud wrote:
> yes, in fact this piece of code has been borrowed from Jama, and they use a
> trick to keep the "eigenvectors" real.
>
> so this is their notes:
>
>     If A is symmetric, then A = V*D*V' where the eigenvalue matrix D is
>     diagonal and the eigenvector matrix V is orthogonal. That is,
>     the diagonal values of D are the eigenvalues, and
>     V*V' = I, where I is the identity matrix.  The columns of V
>     represent the eigenvectors in the sense that A*V = V*D.
>
>    If A is not symmetric, then the eigenvalue matrix D is block diagonal
>     with the real eigenvalues in 1-by-1 blocks and any complex eigenvalues,
>     a + i*b, in 2-by-2 blocks, [a, b; -b, a].  That is, if the complex
>     eigenvalues look like
> <pre>
>
>           u + iv     .        .          .      .    .
>             .      u - iv     .          .      .    .
>             .        .      a + ib       .      .    .
>             .        .        .        a - ib   .    .
>             .        .        .          .      x    .
>             .        .        .          .      .    y
> </pre>
>         then D looks like
> <pre>
>
>             u        v        .          .      .    .
>            -v        u        .          .      .    .
>             .        .        a          b      .    .
>             .        .       -b          a      .    .
>             .        .        .          .      x    .
>             .        .        .          .      .    y
>
>     This keeps V a real matrix in both symmetric and non-symmetric
>     cases, and A*V = V*D.
>
>
> I guess it should be fairly easy to extract the "true" eigenvectors from
> the current ones, but unfortunately, I won't have time to look into it
> soon.
>
> gael.
>
> On Thu, Sep 25, 2008 at 2:33 AM, Timothy Hunter
<tjhunter@xxxxxxxxxxxx>wrote:
> > For your information, the eigen values returned seem correct (as
> > checked with random matrices against matlab's computations). Also, the
> > computed eigen vectors have no imaginary part and are different.
> >
> > On Wed, Sep 24, 2008 at 1:47 PM, Gael Guennebaud
> >
> > <gael.guennebaud@xxxxxxxxx> wrote:
> > > ah, thanks for the fix. Actually it is supposed to work for non
> > > symmetric matrices. At least it worked a while ago. I'll check that
> > > when I'll have time....
> > >
> > > gael.
> > >
> > > On Wed, Sep 24, 2008 at 10:41 PM, Benoît Jacob <jacob@xxxxxxxxxxxxxxx>
> > >
> > > wrote:
> > >> On Wednesday 24 September 2008 22:14:12 Timothy Hunter wrote:
> > >> > Hello,
> > >> > I would like to compute eigen values for non-symmetric matrices. I
> >
> > tried
> >
> > >> > to
> > >> > use to the EigenSolver but it does not compile because it cannot
> > >> > find the
> > >> > function .block(int, int)  (see attached log).
> > >>
> > >> OK, this function was recently renamed to segment(int,int).
> > >> Fixed in r864468.
> > >>
> > >> > Also, the
> > >> > tests for non self-adjoint matrices are disabled in
> >
> > test/eigensolver.cpp
> >
> > >> > .
> > >> > Does it mean this class is not ready yet?
> > >>
> > >> I tried re-enabling this test, and fixed it so it compiled, and the
> >
> > result
> >
> > >> is
> > >> that with a real, non-selfadjoint matrix, the unit-test failed at line
> > >> 117.
> > >> So please consider it as not yet ready for now.
> > >>
> > >> Gael, if it's not yet ready maybe #ifdef it out for now.
> > >>
> > >> Cheers,
> > >> Benoit